Saturday, August 01, 2009

IITs and the reservation policy: A quick look at the JEE-2009 results

Like they did last year, the IITs have released some (but only some!) data on this year's JEE rank-holders. Specifically, we now have data on the aggregate scores at specified ranks for five separate categories: Common Merit List (CML), Other Backward Classes (OBC), Scheduled Castss(SC), Scheduled Tribes (ST) and Physically Disabled (PD). The quick analysis in this post considers only the first four categories: CML, OBC, SC and ST.

This year's procedure for assigning ranks is similar to that used last year: in the first stage, students with very low marks -- those scoring less than the subject-wise cut-off marks in any of the three subjects: math, physics and chemistry -- are removed from consideration, and in the second stage, the top N (this year, N = 8295 in the common list; about 1700 more appear in the OBC and other such lists) of the rest are ranked according to the aggregate score. There is, however, one difference between 2008 and 2009; this difference is in the cut-off marks used for first stage: Last year, the cut-off eliminated the bottom 20 percentile in each subject, while this year, it eliminated those with lower than the subject average.

This year's subject-wise cut-offs were 11, 8 and 11 (out of 160) in math, physics and chemistry, respectively. I checked, but couldn't find, the actual number of students who survived the first filter.

The aggregate scores of the first 500 ranks span a range of 122 (424 to 302), and those for the next 500 span just 24 (302 to 278). The remaining 7290 ranks span a range of just 100 marks!

At the 1000th rank, a difference of 1 mark (out of 480) could set a student back by 30 ranks. At ranks 5000+, each mark is worth as many as 125 ranks!

The cut-off marks -- both at the subject level and at the aggregate level -- are lower for reserved category students. For OBC, this relaxation is 10 percent, and for SC, ST and PD, it is 50 percent.

Thus, the aggregate score of the last OBC candidate is at 161 compared to 178 for the last candidate in the common list; similarly, it's 89 for SC,ST and PD categories.

All the lists put together, 10,035 students were eligible to stake a claim for a seat in one of the institutions participating in JEE.

Let's look at some of the information graphically. Here's the first plot, which just presents the raw data on rank within a category against the aggregate marks.

Figure 1

Figure 1 is not very useful because of our system of reservation in which the top 10 percent of the SC students, for example, study -- or, at least, have the opportunity to study -- in the same class as the top 10 percent in each of the other categories. Thus, a more useful way of looking at the data is to use scaled plots, where the rank within a category is divided by the last rank (the highest rank number) in that category: thus for the candidates in the OBC category, the modified y-axis now represents the OBC rank divided by the last OBC rank (1930); thus all the four curves end at 1.0.

Here's that figure, with the scaled rank (within category) plotted against the aggregate score.

Figure 2

This plot, while better than Figure 1, still has some problems. For example, the curves for SC and ST appear close together in this figure, but in reality there's a big gap in the rates at which SC and ST candidates get ranked in JEE. The figure hides the crucial fact that while the OBC, SC and ST quotas are not completely filled, there is significant difference in the "degree of incompleteness" among the three categories.

This becomes clearer when we look at the actual number of candidates who make it to the OBC, SC and ST lists: 1930, 967 and 208, respectively. Clearly, they are below their full-quota figures of 2700, 1500 and 750 (for this calculation, I have conservatively assumed the total number of rank-holders to be 10,000; with full quota, this number would be more than 10,035). In other words, only 72%, 65% and 28% of the seats reserved for OBC, SC and ST candidates may get filled this year.

Let's re-do the figure using these numbers (full-quota) for scaling the ranks. The result is in Figure 3. Since the ranks within each category are now scaled using a larger number, the curves do not go all the way to 1.0 at the left-top.

Figure 3

While Figures 2 and 3 look roughly the same for CML and OBC, a difference does emerge for SC and ST categories; and it shows, graphically, the extent to which ST students lag behind SC students.

What is striking is how the left-most ends of all the curves appear roughly parallel to one another. This allows us to put a figure on how much the reserved category candidates need to "catch" up. At comparable category-wise percentiles, the aggregate marks of OBC, SC and ST candidates trail those in CML by 25, 120 and 150 marks. Since the maximum aggregate score is 480, these numbers translate to a group disadvantage of about 5%, 25% and 30%, respectively.

[I readily admit that Figure 3 could be improved with better estimates for the total number of candidates in the full-quota scenario; but the results (especially the estimates of the differences between CML and the reserved categories) are unlikely to be affected much.]

As I said, these observations are broadly in line with what we found in JEE-2008. In particular, the OBC scores are just about 5 % below those of the common pool; thus, someone at the n-th percentile in the OBC list wouldn't suffer a serious disadvantage with respect to a classmate who's at the same n-th percentile in the common list.

Unfortunately (and as I noted last year), this is not the case for SC and ST students; if they go for the "top" IIT-branch combination that they are eligible for, they are likely to find themselves competing with folks whose JEE scores are far higher than theirs. Our quick analysis tells us that they are better off choosing "lower" branches than they are eligible for.

From what I know (or hear from my friends in IITs), these broad conclusions are generally borne out in real life. OBC students, on average, do just about as well as the rest of the class; on the other hand, SC and ST students, on average, do somewhat worse than the class average.

* * *

Update: Out of 1930 students who make it to the OBC list, about 1400 would have made it to the common list without needing a relaxed cut-off. In other words, 14% of the available seats would have gone to the OBC students anyway; this figure was the same last year too. Thus, a relaxation of 10% in the cut-off marks (both at the subject level and in the aggregate) gets OBCs only an additional 500 seats (or, 5% additional seats).

And here's the thing: the IITs will probably keep this relaxation in cut-off marks at 10%. If the ratio (10% relaxation to 5% additional OBC seats) holds, this would imply that OBCs' share of IIT seats will settle at about 19-20%, and that this share can go up only if the OBCs get into the common pool in greater numbers.

@Cipher: I'm glad you are satisfied with the results of our reservation policy ... ;-)

@Niket: I agree that ranking a large number of students (nearly 10000) using just 480 marks is impossible without serious overlap at each mark. BTW, in my post, the passage you quoted appears only as an observation; I don't wish to attach a value judgment to it.

However, I really have to wonder why each question should carry the same weight irrespective of its difficulty level. I have always suspected that if the JEE's ranking procedure is put through even a low level statistical test, the results would be appalling; for example, the 'validity' of any JEE rank beyond 1000 (say) would be highly questionable.

One way out, as you suggest (and as I and others have suggested), would be to admit students into IITs without assigning a branch. It would be wonderful if the IITs were to implement this scheme.

I am not able to understand how assigning branches in second year will make the rankings more transparent. One it will be the rankings that will decide which college a person will get. Probably increasing the marks is a much better way.Second it will be unfair to take away the advantages of raking higher. Third it will make first year much more growling for students. They need to relook the focus on studies after atleast 2 years of hard work. Its not just the marks that matter, but other activities also matter.

SIR , MAY I KNOW ABOUT RESERVATION FOR PD STUDENTS IN IIT'S? I READ YOUR BLOG . WHAT ARE THE DOCUMENTS REQUIRED FOR ADMISSION THROUGH THIS QUOTA? I AM PD STUDENT WITH 40% DISABILITY? PLEASE HELP ME . I AM PREPARING FOR JEE 2011.